As demonstrated, the maximal determinant problem for \(n \equiv 0 \bmod 4\)  is extensive.
Paley conjectured in the 1930s that the bound is attained in every dimension divisible by 4.
We note that Hadamard matrices have found application in the construction of error-correcting codes,
experimental designs and more recently in the design of quantum algorithms. The reader is referred to the
monographs of Horadam [1]} and Bengtsson and Zyczkowski [2]} for further details.
